Answer: 16 miles.
Explanation:
Let's define:
Vincent's house is in the position 0 mi in a number line.
We know that the post office is 1 mile west of Vincent's house, if we define west as the positive side of the number line, then the position of the post office is:
0mi + 1mi = 1mi
(position of Vincent's house plus one mile)
And we know that the 11 library is 15 miles west from the post office, then the position of this library is:
1mi + 15mi = 16mi
(position of the post office plus 15 miles)
The distance between Vincent's house and the library is equal to the difference between the positions, where we can remember that the position of Vincent's house is 0mi, and the position of the library is 16mi
Distance = 16mi - 0 mi = 16mi
This means that the library is 16 miles away from Vincent's house.